Answer: The values of......
[tex]f(-5)=\frac{9}{4}\\ \\ f(-2)= -1\\ \\ f(4)=0[/tex]
Step-by-step explanation:
Given function is: [tex]\left \{ {{f(x)= \frac{1}{4}x^2 -4, if x\neq -2} \atop {=-1, if x=-2}} \right.[/tex]
For [tex]f(-5),[/tex] the value of [tex]x[/tex] is -5, which is not equal to -2.
So, [tex]f(-5)= \frac{1}{4}(-5)^2 -4 = \frac{1}{4}(25)-4 =\frac{25}{4}-4=\frac{25-16}{4}=\frac{9}{4}[/tex]
For [tex]f(-2),[/tex] the value of [tex]x[/tex] is -2.
So, [tex]f(-2)= -1[/tex]
For [tex]f(4),[/tex] the value of [tex]x[/tex] is 4, which is not equal to -2.
So, [tex]f(4)=\frac{1}{4}(4)^2 -4 =\frac{1}{4}(16)-4 =4-4=0[/tex]
